TAMPA — A new, more-conciliatory phase may be opening up in the contentious fight between taxi regulators in Hillsborough County and the ride-sharing upstarts Lyft and Uber.

Officials with the Public Transportation Commission have begun talks with at least one of the ride-sharing companies to find a “middle ground” that could allow the unregulated car service to operate inside the law in Hillsborough County, according to the agency’s executive director, Kyle Cockream.

“We’re trying to work through some things, but this is not a short-term process,” Cockream said. He declined to identify which of the companies he was talking with most recently, but did confirm he has talked to Lyft officials about several matters, such as insurance coverage. There is a long list of factors involved, Cockream said, primarily because Lyft and Uber operate so differently from taxi and limousine companies.

Taxi companies must receive a license from the PTC, get their vehicles inspected, and their drivers must pass background checks and charge PTC-approved rates.

By contrast, Lyft and Uber operate as something between a taxi and a friend with a car. Drivers with Lyft or Uber go through that company’s background check. Customers with a Lyft or Uber app on their smartphone request rides, with the fees based on the company’s rates and paid through the app system. Lyft and Uber also position themselves as a type of social network where passengers and drivers sign up in part to meet new friends.

A starting point is working on a few easier factors, he said.

The cars in use would likely pass a PTC inspection, if drivers sought them, and Lyft has been seeking out more insurance that would cover the driver and passenger in an accident. Setting up a Florida-based background check system should also be straightforward, he said.

That’s not to say a solution is just around the corner.

First, Cockream said, he would need to negotiate a preliminary deal with the ride-sharing companies. Then, if those talks succeeded, he would need to bring the proposed deal to the PTC board, issue public notice of any potential board meeting on the issue, and then the PTC would have to formally act.

Officials with Lyft and Uber have said they look forward to working with local authorities, and they have a big booster in Tampa Mayor Bob Buckhorn.

Unfortunately for Lyft and Uber, the city has no formal role in day-to-day operations of the PTC, which was established by state law and operates under its own jurisdiction.